About the Project

error bounds

AdvancedHelp

(0.002 seconds)

11—20 of 75 matching pages

11: 3.2 Linear Algebra
Then we have the a posteriori error bound
12: 9.7 Asymptotic Expansions
§9.7(iii) Error Bounds for Real Variables
In (9.7.7) and (9.7.8) the n th error term is bounded in magnitude by the first neglected term multiplied by χ ( n + σ ) + 1 where σ = 1 6 for (9.7.7) and σ = 0 for (9.7.8), provided that n 0 in the first case and n 1 in the second case. …
§9.7(iv) Error Bounds for Complex Variables
The n th error term in (9.7.5) and (9.7.6) is bounded in magnitude by the first neglected term multiplied by … Corresponding bounds for the errors in (9.7.7) to (9.7.14) may be obtained by use of these results and those of §9.2(v) and their differentiated forms. …
13: 6.12 Asymptotic Expansions
For these and other error bounds see Olver (1997b, pp. 109–112) with α = 0 . …
14: Bibliography Z
  • J. M. Zhang, X. C. Li, and C. K. Qu (1996) Error bounds for asymptotic solutions of second-order linear difference equations. J. Comput. Appl. Math. 71 (2), pp. 191–212.
  • 15: 30.9 Asymptotic Approximations and Expansions
    For uniform asymptotic expansions in terms of Airy or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1986). … For uniform asymptotic expansions in terms of elementary, Airy, or Bessel functions for real values of the parameters, complex values of the variable, and with explicit error bounds see Dunster (1992, 1995). …
    16: Bibliography T
  • J. G. Taylor (1978) Error bounds for the Liouville-Green approximation to initial-value problems. Z. Angew. Math. Mech. 58 (12), pp. 529–537.
  • J. G. Taylor (1982) Improved error bounds for the Liouville-Green (or WKB) approximation. J. Math. Anal. Appl. 85 (1), pp. 79–89.
  • 17: 2.9 Difference Equations
    For error bounds see Zhang et al. (1996). … For error bounds see Zhang et al. (1996). … Error bounds and applications are included. …
    18: Bibliography D
  • T. M. Dunster (1996b) Asymptotics of the generalized exponential integral, and error bounds in the uniform asymptotic smoothing of its Stokes discontinuities. Proc. Roy. Soc. London Ser. A 452, pp. 1351–1367.
  • T. M. Dunster (1996c) Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one. Methods Appl. Anal. 3 (1), pp. 109–134.
  • T. M. Dunster (2014) Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.
  • 19: 8.11 Asymptotic Approximations and Expansions
    Sharp error bounds and an exponentially-improved extension for (8.11.7) can be found in Nemes (2016). … For error bounds and an exponentially-improved extension for this later expansion, see Nemes (2015c). … For sharp error bounds and an exponentially-improved extension, see Nemes (2016). …
    20: 10.41 Asymptotic Expansions for Large Order
    For derivations of the results in this subsection, and also error bounds, see Olver (1997b, pp. 374–378). … In the case of (10.41.13) with positive real values of z the result is a consequence of the error bounds given in Olver (1997b, pp. 377–378). … This is a consequence of the error bounds associated with these expansions. …